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Simplifying (7 + 8i)(6 + 9i) = 0 Multiply (7 + 8i) * (6 + 9i) (7(6 + 9i) + 8i * (6 + 9i)) = 0 ((6 * 7 + 9i * 7) + 8i * (6 + 9i)) = 0 ((42 + 63i) + 8i * (6 + 9i)) = 0 (42 + 63i + (6 * 8i + 9i * 8i)) = 0 (42 + 63i + (48i + 72i2)) = 0 Combine like terms: 63i + 48i = 111i (42 + 111i + 72i2) = 0 Solving 42 + 111i + 72i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(14 + 37i + 24i2) = 0 Factor a trinomial. 3((7 + 8i)(2 + 3i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + 8i)' equal to zero and attempt to solve: Simplifying 7 + 8i = 0 Solving 7 + 8i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 8i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 8i = 0 + -7 8i = 0 + -7 Combine like terms: 0 + -7 = -7 8i = -7 Divide each side by '8'. i = -0.875 Simplifying i = -0.875Subproblem 2
Set the factor '(2 + 3i)' equal to zero and attempt to solve: Simplifying 2 + 3i = 0 Solving 2 + 3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3i = 0 + -2 3i = 0 + -2 Combine like terms: 0 + -2 = -2 3i = -2 Divide each side by '3'. i = -0.6666666667 Simplifying i = -0.6666666667Solution
i = {-0.875, -0.6666666667}
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